rajathpanta wrote:

What is the greatest distance between two points in a cylinder where the area of the base is 9 pi and height is 5?

A. \(\sqrt{34}\)

B. \(\sqrt{48}\)

C. \(\sqrt{61}\)

D. \(\sqrt{76}\)

E. \(\sqrt{106}\)

We see that the greatest distance in a cylinder is a diagonal line from one base to the other, or in other words, the hypotenuse of a right triangle, with the height of the cylinder being the height of the triangle and the diameter of the base being the base of the triangle. Let’s determine the diameter.

Since the area of the base is 9π:

area = πr^2

9π = πr^2

9 = r^2

3 = r

So, the diameter is 6. Recall that the height of the cylinder is 5, so we can determine the length of the diagonal using the Pythagorean theorem:

6^2 + 5^2 = d^2

36 + 25 = d^2

61 = d^2

√61 = d

Answer: C

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